Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth

Michał Włodarczyk

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In Chordal/Interval Vertex Deletion we ask how many vertices one needs to remove from a graph to make it chordal (respectively: interval). We study these problems under the parameterization by treewidth tw of the input graph G. On the one hand, we present an algorithm for Chordal Vertex Deletion with running time 2O(tw) · |V(G)|, improving upon the running time 2O(tw2)·|V(G)|O(1) by Jansen, de Kroon, and Włodarczyk (STOC’21). When a tree decomposition of width tw is given, then the base of the exponent equals 2ω−1·3+1. Our algorithm is based on a novel link between chordal graphs and graphic matroids, which allows us to employ the framework of representative families. On the other hand, we prove that the known 2O(tw log tw) · |V(G)|-time algorithm for Interval Vertex Deletion cannot be improved assuming Exponential Time Hypothesis.

Original languageEnglish
Title of host publication50th International Colloquium on Automata, Languages, and Programming, ICALP 2023
EditorsKousha Etessami, Uriel Feige, Gabriele Puppis
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772785
DOIs
StatePublished - 1 Jul 2023
Event50th International Colloquium on Automata, Languages, and Programming, ICALP 2023 - Paderborn, Germany
Duration: 10 Jul 202314 Jul 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume261
ISSN (Print)1868-8969

Conference

Conference50th International Colloquium on Automata, Languages, and Programming, ICALP 2023
Country/TerritoryGermany
CityPaderborn
Period10/07/2314/07/23

Keywords

  • chordal graphs
  • fixed-parameter tractability
  • interval graphs
  • matroids
  • representative families
  • treewidth

ASJC Scopus subject areas

  • Software

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